Minimization of -Sensitivity for State-Space Digital Filters Subject to -Dynamic-Range Scaling Constraints

The problem of minimizing an -sensitivity measure subject to -norm dynamic-range scaling constraints for state- space digital filters is formulated. It is shown that the problem can be converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algorithm with closed-form formula for gradient evaluation. The coordinate transformation matrix obtained is then used to construct the op- timal state-space filter structure that minimizes the -sensitivity measure subject to the scaling constraints. A numerical example is presented to illustrate the utility of the proposed technique.